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After solving for the ratio itself (discussed in the calculations section), we can find that the golden ratio is: | After solving for the ratio itself (discussed in the calculations section), we can find that the golden ratio is: | ||
| − | <center> <math> \frac{1 \pm \sqrt{5}}{2} = \phi </math> </center> | + | <center> <math> \frac{1 \pm \sqrt{5}}{2} = \phi = 1.618 </math> </center> |
The golden ratio, <math>\phi</math>, is sometimes also called the golden mean or the golden section. The golden ratio can be frequently observed in man-made objects, though they are generally “imperfectly golden” – that is, the ratio is approximately the golden ratio, but not exactly. Some everyday examples include: credit cards, <math>\frac{w}{h}=1.604</math>, and laptop screens, <math>\frac{w}{h}=1.602</math> (Tannenbaum 392). | The golden ratio, <math>\phi</math>, is sometimes also called the golden mean or the golden section. The golden ratio can be frequently observed in man-made objects, though they are generally “imperfectly golden” – that is, the ratio is approximately the golden ratio, but not exactly. Some everyday examples include: credit cards, <math>\frac{w}{h}=1.604</math>, and laptop screens, <math>\frac{w}{h}=1.602</math> (Tannenbaum 392). | ||
Revision as of 16:45, 2 December 2018
Introduction
The golden ratio is a ratio such that, given two quantities a and b,
After solving for the ratio itself (discussed in the calculations section), we can find that the golden ratio is:
The golden ratio, $ \phi $, is sometimes also called the golden mean or the golden section. The golden ratio can be frequently observed in man-made objects, though they are generally “imperfectly golden” – that is, the ratio is approximately the golden ratio, but not exactly. Some everyday examples include: credit cards, $ \frac{w}{h}=1.604 $, and laptop screens, $ \frac{w}{h}=1.602 $ (Tannenbaum 392).
Visualizations of the golden ratio can be seen below (Weisstein):
MathIsFun also has an interactive display that can construct a rectangle in the golden ratio given a certain fixed width or length.
